GATE Mechanical Engineering (ME) 2017 Shift 1 Solved Paper

An initially stress-free massless elastic beam of length L and circular cross-section with diameter d (d ≪ L) is held fixed between two walls as shown. The beam material has Young’s modulus E and coefficient of thermal expansion α. If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to